The present invention relates to a method for analyzing characteristics of a magnetic transducer such as an electromagnetic field characteristics and an magnetization characteristics of a magnetic transducer such as an inductive magnetic recording head for example.
With the recent widespread use of personal computers, networked information is rapidly increasing. Such information includes not only conventional numerical data but also, for example, image data, and the volume of the information is increasing dramatically. Handling such an enormous amount of information requires a high-speed MPU as well as a high-speed, large-capacity, and high-reliability hard disk system.
When information is recorded magnetically on a recording medium such as a hard disk, a magnetic head having a coil wound around a soft magnetic material is used. With a so-called longitudinal recording medium that has an easy axis of magnetization in an in-plane direction, recording is achieved by the use of a leakage magnetic flux from a minute gap between two magnetic poles of a magnetic head made of a soft magnetic material. For this reason, the recording performance of a magnetic recording medium depends greatly not only on the characteristics of the medium but also on various factors that influence the recording magnetic field.
The factors that influence the recording magnetic field include primarily a film for protecting a magnetic medium and a head, a thickness of lubricant layer, a recess of a head magnetic pole, a magnetic spacing between the head and the medium that is determined by a floating height of the head, a length of a gap, magnetic poles, a magnetomotive force of a coil, and ICs and electrical circuits of a recording driver. Among these factors, a shape, magnetic characteristics, and magnetization structure of the head magnetic poles are important parameters in designing a magnetic head.
Conventionally, the design of a magnetic head often uses analysis based on a computer simulation. Computer-based analysis is used for performing an accurate, quick and quantitative analysis. This type of computer simulation has been a predominant tool in designing a magnetic head (Journal of Japanese Applied Magnetism Institute, Vol. 25, No. 3-1, pp.133-148, 2001).
In the design of a magnetoresistive effect (MR) read head, magnetic analysis is performed by using a micro-magnetic simulation (IEEE Trans Magn., Vol. 34, No. 4, p1516, 1998). For anisotropic magnetoresistive effect (AMR) heads, this method divides only an MR film and its soft adjacent layer (SAL) into elements, and for spin valve MR heads, only free layer and pin layer into elements. Then, based on an effective magnetic field that is the sum of a static magnetic field, an anisotropic magnetic field, an exchange magnetic field, and an external magnetic field, the Landau-Lifshitz-Gilbert (LLG) equation is solved for the magnetization in the elements (Jpn. J. Appl. Phys., 28, p2485, 1989). In this method, the static magnetic field calculation of which is the most time-consuming is determined by an integral equation method (IEM).
For the analysis of a magnetic recording head, only electromagnetic field analysis is performed by using finite element method (FEM), finite difference time domain method (FDTD method), integral equation method (IEM), or boundary element method, but no magnetization analysis is executed because a time required for this calculation is too long to complete analysis.
For an MR read head, only a very thin film is discreted, which has a pattern size of about 1 xcexcm2 and a thickness of no more than 0.1 xcexcm. Therefore, the calculation of a static magnetic field requires only a small-scale calculation that involves elements of an order of 1000, so that a time required for calculating the static magnetic field is very short. In contrast to this, for a magnetic recording head, magnetic poles of a complex shape with a pattern size of several tens xcexcm2 and a thickness of the order of micro meters are divided into elements, so that the number of the elements is enormous ranging from several tens thousand to several hundreds thousand. Moreover, in order to consider eddy current effect, the depth of skin of a magnetic body should be expressed. Thus, it is inevitable that the region is divided into even smaller elements, and therefore the calculation of static magnetic field requires a longer time for each cycle of calculation for the magnetic recording head.
When the magnetization M in a steady state is calculated, the magnetization M is required to be calculated one by one self consistently and the static magnetic field needs to be calculated every time the magnetization M is updated. When the static magnetic field is calculated by the IEM that is used in the micromagnetic simulation, the time required for calculating the static magnetic field is proportional to N3, N being the number of elements. Thus, repetitively effecting the IEM calculation every time the magnetization is updated takes an enormous time for one-time calculation of magnetization unless each cycle of the calculation of the static magnetic field is short. Thus, for a magnetic recording head, the time required for calculation is so long that even a today""s super computer is not enough. For this reason, magnetization analysis that requires multiple calculations of static magnetic field is not carried out. Thus, for the magnetic recording head, only an electromagnetic field analysis that requires a smaller number of magnetic field calculations is performed.
However, the shape of magnetic poles and magnetic characteristics such as anisotropy and magnetostriction of the magnetic poles determine magnetization structure, and influence the ability of the magnetic recording head seriously, so that analysis in terms of magnetization has been desired in analyzing a magnetic recording head.
It is therefore an object of the invention to provide a method and a program for analyzing characteristics that are capable of analyzing the magnetization of a magnetic transducer such as a magnetic recording head.
According to the present invention, a method for analyzing characteristics of a magnetic transducer includes a step of sub-dividing a region to be analyzed, in a magnetic transducer into a plurality of polyhedral elements, based on at least data representing a shape of the region in the magnetic transducer, and a step of performing a transient calculation. The transient calculation includes calculating a transient electric field of each of the plurality of polyhedral elements by using a conductivity and a dielectric constant of each of the plurality of polyhedral elements, a transient electric field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient magnetic field of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a current density of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), calculating a transient magnetic field of each of the plurality of polyhedral elements by using a transient magnetic field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient electric field of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a magnetic permeability of each of the plurality of polyhedral elements, and updating the magnetic permeability in accordance with a magnetic flux density determined from the calculated transient magnetic field. The step of performing transient calculation is repeated until a predetermined number of time steps have been completed, to determine electric fields and magnetic fields of all of the plurality of polyhedral elements in the region to be analyzed.
For each of polyhedral elements, a transient electric field and a magnetic field are calculated one alternately with the other by shifting xc2xd of time step on the basis of the current density of each polyhedral element and material constants including a magnetic permeability of each polyhedral element. In this manner, electric fields and magnetic fields of all polyhedral elements in a region to be analyzed are determined, and the magnetic permeability is updated in accordance with a magnetic flux density determined from the magnetic field calculated each time. This updated magnetic permeability is used to calculate a magnetic field at the following time step. By this method, the electric field can be analyzed taking magnetic saturation into account.
It is preferred that the step of performing transient calculation includes determining a magnetic flux density of each of the plurality of polyhedral elements from the calculated transient magnetic field, and updating the magnetic permeability to a magnetic permeability obtained from a magnetic flux density using a predetermined magnetic permeability-magnetic flux density characteristic.
It is also preferred that the step of performing transient calculation includes providing secondary absorption boundary conditions to the calculated transient electric field at a boundary of the region to be analyzed, by using the transient electric field calculated at two preceding time steps (2xcex94t) and the transient electric field calculated at one preceding time step (xcex94t).
It is preferred that the transient electric field En is calculated by       E    n    =                              1          -                                    σΔ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                                1          +                                    σ              ⁢                              xe2x80x83                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                          ⁢              E                  n          -          1                      +                                        Δ            ⁢                          xe2x80x83                        ⁢            t                    ϵ                          1          +                                    σ              ⁢                              xe2x80x83                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                          ⁢              ∇                  xc3x97                      H                          n              -                              1                /                2                                                          -                                        Δ            ⁢                          xe2x80x83                        ⁢            t                    ϵ                          1          +                                    σΔ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                          ⁢              J                  n          -                      1            /            2                              
where "sgr" is the conductivity, xcex5 is eth dielectric constant, xcex94t is a time step, Hnxe2x88x921/2 is a magnetic field at xc2xd preceding time step and Jnxe2x88x921/2 is a current density at xc2xd preceding time step.
It is also preferred that the transient magnetic field Hn+1/2 is calculated by       H          n      +              1        /        2              =            H              n        -                  1          /          2                      -                            Δ          ⁢                      xe2x80x83                    ⁢          t                μ            ⁢              ∇                  xc3x97                      E            n                                -                            Δ          ⁢                      xe2x80x83                    ⁢          t                μ            ⁢              J        m        n            
where xcexc is the magnetic permeability and Jmn is a magnetizing current at xc2xd preceding time step.
According to the present invention further a method of analyzing characteristics of a magnetic transducer, includes a step of sub-dividing a region to be analyzed, in a magnetic transducer into a plurality of polyhedral elements, based on at least data representing a shape of the region in the magnetic transducer, and a step of performing a transient calculation. The transient calculation includes calculating a transient electric field of each of the plurality of polyhedral elements by using a conductivity and a dielectric constant of each of the plurality of polyhedral elements, a transient electric field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient magnetic field of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a current density of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), calculating a transient magnetic field of each of the plurality of polyhedral elements by using a transient magnetic field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient electric field of each of the plurality of polyhedral elements, at xc2xd preceding time step (xcex94t/2), and a magnetizing current corresponding to a magnetization of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), calculating an effective magnetic field of each of the plurality of polyhedral elements, from the calculated transient magnetic field, and determining a derivative of magnetization of each of the plurality of polyhedral elements, by using the calculated effective magnetic field to calculate a magnetization at that time. The step of performing transient calculation is repeated until a predetermined number of time steps have been completed, to determine electric fields, magnetic fields and magnetizations of all of the plurality of polyhedral elements in the region to be analyzed.
Electric field E, magnetic field H and magnetization M are obtained simultaneously by using a FDTD method and a LLG equation in such a way that time steps for the FDTD method and the LLG equation are synchronized with each other. In other words, a transient electric field En is calculated based on the conductivity "sgr" and the dielectric constant xcex5 of each of the polyhedral elements, an electric field Enxe2x88x921 of each of the polyhedral elements, calculated at one preceding time step (xcex94t), a magnetic field Hnxe2x88x921/2 of each of the polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a current density Jnxe2x88x921/2 of each of the polyhedral elements, at xc2xd preceding time step (xcex94t/2). Then, a transient magnetic field Hn+1/2 of each of polyhedral elements is calculated on the basis of a transient magnetic field Hnxe2x88x921/2 of each of the polyhedral elements, calculated at one preceding time step (xcex94t), a transient electric field En of each of the polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a magnetizing current Jmn determined from a magnetization of each of the polyhedral elements, calculated at one preceding time step (xcex94t).
As mentioned previously, the method of calculating magnetic field includes finite element method (FEM), finite difference time domain method (FDTD method), and integral equation method (IEM). As listed in Table 1, the time required for calculation is proportional to N3 for the IEM where N is the number of elements, Nxc3x97bandwidth (BW) for the FEM, and N4/3 for the FDTD method.
Thus, in the FDTD method, an increase in calculation time is minimum when the number of elements is increased, i.e., the FDTD method requires less calculation time than conventional methods and is practical.
In the IEM and the FEM, an electromagnetic field at steady state is determined at a certain time. In the FDTD method, transient states of electromagnetic field are calculated one by one at respective time steps until the calculation arrives at a certain value. In other words, the basic equations of the FDTD method are expressed in terms of derivatives of electric field and magnetic field with respect to time as shown in Equations (1) and (2).                                           ∂            E                                ∂            t                          =                                            -                              σ                ϵ                                      ⁢            E                    +                                    1              ϵ                        ⁢                          ∇                              xc3x97                H                                              -                                    1              ϵ                        ⁢            J                                              (        1        )                                                      ∂            H                                ∂            t                          =                                            -                              1                μ                                      ⁢                          ∇                              xc3x97                E                                              -                                    1              μ                        ⁢                          xe2x80x83                        ⁢                          J              m                                                          (        2        )            
These equations indicate that the rotation of a magnetic field creates an electric field, and the rotation of an electric field creates a magnetic field. Here, "sgr" is a conductivity, xcex5 is a dielectric constant, xcexc is a magnetic permeability, J is a current density and Jm is a magnetizing current.
When magnetization is calculated in micromagnetics, the LLG equation in the form of Equation (3) is used. Here, xcex94M is a derivative of magnetization, xcex1 is a damping constant, xcex3 is a gyro constant, M is a magnetization, Heff is an effective magnetic field given by Equation (4), H is a transient magnetic field calculated by the FDTD method and is a sum of static magnetic field and current magnetic field, Hk is anisotropy magnetic field, and Hex is exchange magnetic field.                                           (                          1              +                              α                2                                      )                    ⁢                                    ∂              M                                      ∂              t                                      =                                            -                              "LeftBracketingBar"                γ                "RightBracketingBar"                                      ⁢                          (                              M                xc3x97                                  H                  eff                                            )                                -                                                    α                ⁢                                  "LeftBracketingBar"                  γ                  "RightBracketingBar"                                            M                        ⁡                          [                              M                xc3x97                                  (                                      M                    xc3x97                                          H                      eff                                                        )                                            ]                                                          (        3        )            xe2x80x83Heff=H+Hk+Hexxe2x80x83xe2x80x83(4)
The LLG equation is also expressed in terms of a derivative of magnetization with respect to time, and transient states require to be calculated one by one in order to determine a value in the steady state which is a final state. Thus, by using Equations (1) to (3) as calculus of finite difference, the time step of the FDTD method and the LLG equation are synchronized, so that the electric field E, magnetic field H, and magnetization M may be solved. By using the thus obtained electric field E, magnetic field H, magnetization M, and gyro constant, ferromagnetic resonance frequency can be determined. As mentioned above, the present invention provides the transient states and steady states of electric field E, magnetic field H, and magnetization M, and ferromagnetic resonance frequency.
It is preferred that the step of performing transient calculation includes providing secondary absorption boundary conditions to the calculated transient electric field at a boundary of the region to be analyzed, by using the transient electric field calculated at two preceding time steps (2xcex94t) and the transient electric field calculated at one preceding time step (xcex94t).
It is also preferred that the transient electric field En is calculated by       E    n    =                              1          -                                    σΔ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                                1          +                                    σ              ⁢                              xe2x80x83                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                          ⁢              E                  n          -          1                      +                                        Δ            ⁢                          xe2x80x83                        ⁢            t                    ϵ                          1          +                                    σ              ⁢                              xe2x80x83                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                          ⁢              ∇                  xc3x97                      H                          n              -                              1                /                2                                                          -                                        Δ            ⁢                          xe2x80x83                        ⁢            t                    ϵ                          1          +                                    σΔ              ⁢                              xe2x80x83                            ⁢              t                                      2              ⁢              ϵ                                          ⁢              J                  n          -                      1            /            2                              
where "sgr" is the conductivity, xcex5 is eth dielectric constant, xcex94t is a time step, Hnxe2x88x921/2 is a magnetic field at xc2xd preceding time step and Jnxe2x88x921/2 is a current density at xc2xd preceding time step.
It is further preferred that the transient magnetic field Hn+1/2 is calculated by       H          n      +              1        /        2              =            H              n        -                  1          /          2                      -                            Δ          ⁢                      xe2x80x83                    ⁢          t                μ            ⁢              ∇                  xc3x97                      E            n                                -                            Δ          ⁢                      xe2x80x83                    ⁢          t                μ            ⁢              J        m        n            
where xcexc is the magnetic permeability and Jmn is a magnetizing current at xc2xd preceding time step.
It is preferred that a derivative xcex94M of the magnetization is calculated by             (              1        +                  α          2                    )        ⁢                  ∂        M                    ∂        t              =                    -                  "LeftBracketingBar"          γ          "RightBracketingBar"                    ⁢              (                  M          xc3x97                      H            eff                          )              -                            α          ⁢                      "LeftBracketingBar"            γ            "RightBracketingBar"                          M            ⁡              [                  M          xc3x97                      (                          M              xc3x97                              H                eff                                      )                          ]            
where xcex1 is a damping constant, xcex3 is a gyro constant, Heff is the effective magnetic field and M is the magnetization.
It is also preferred that the effective magnetic field Heff is calculated by Heff=H+Hk+Hex, where H is the calculated transient magnetic field, Hk is an anisotropy magnetic field and Hex is an exchange magnetic field.
According to the present invention, further, a program for analyzing characteristics of a magnetic transducer brings a computer into a function of sub-dividing a region to be analyzed, in a magnetic transducer into a plurality of polyhedral elements, based on at least data representing a shape of the region in the magnetic transducer, and a function of performing a transient calculation. The transient calculation includes calculating a transient electric field of each of the plurality of polyhedral elements by using a conductivity and a dielectric constant of each of the plurality of polyhedral elements, a transient electric field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient magnetic field of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a current density of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), calculating a transient magnetic field of each of the plurality of polyhedral elements by using a transient magnetic field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient electric field of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a magnetic permeability of each of the plurality of polyhedral elements, and updating the magnetic permeability in accordance with a magnetic flux density determined from the calculated transient magnetic field. The function of performing transient calculation is repeated until a predetermined number of time steps have been completed, to determine electric fields and magnetic fields of all of the plurality of polyhedral elements in the region to be analyzed.
According to the present invention, still further, a program for analyzing characteristics of a magnetic transducer brings a computer into a function of sub-dividing a region to be analyzed, in a magnetic transducer into a plurality of polyhedral elements, based on at least data representing a shape of the region in the magnetic transducer, and a function of performing a transient calculation. The transient calculation includes calculating a transient electric field of each of the plurality of polyhedral elements by using a conductivity and a dielectric constant of each of the plurality of polyhedral elements, a transient electric field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient magnetic field of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), and a current density of each of the plurality of polyhedral elements, calculated at xc2xd preceding time step (xcex94t/2), calculating a transient magnetic field of each of the plurality of polyhedral elements by using a transient magnetic field of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), a transient electric field of each of the plurality of polyhedral elements, at xc2xd preceding time step (xcex94t/2), and a magnetizing current corresponding to a magnetization of each of the plurality of polyhedral elements, calculated at one preceding time step (xcex94t), calculating an effective magnetic field of each of the plurality of polyhedral elements, from the calculated transient magnetic field, and determining a derivative of magnetization of each of the plurality of polyhedral elements, by using the calculated effective magnetic field to calculate a magnetization at that time. The function of performing transient calculation is repeated until a predetermined number of time steps have been completed, to determine electric fields, magnetic fields and magnetizations of all of the plurality of polyhedral elements in the region to be analyzed.
Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings.